Abstract

With phase-shifting joint transform correlation (PSJTC) one uses multiple phase shifts to recover the phase difference between Fourier transforms of the input and the reference. In PSJTC systems the resulting phase-only function is used instead of the joint transform power spectrum (JTPS). Provided it can be recorded linearly, the JTPS reduces to a modulated sinusoidal fringe, especially when the target image matches the reference image. In practice, the JTPS has a wide dynamic range, and a CCD camera has a nonlinear response. Correspondingly, the recorded JTPS turns out to be different from a perfect sinusoidal fringe. Here we study the dynamic range effects of realizing PSJTC with the phase-iterative algorithm.

© 1999 Optical Society of America

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References

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  1. C. S. Weaver, J. W. Goodman, “Technique for optically convolving two functions,” Appl. Opt. 5, 1248–1249 (1966).
    [CrossRef] [PubMed]
  2. F. T. S. Yu, X. J. Lu, “A real-time programmable joint transform correlator,” Opt. Commun. 52, 10–16 (1984).
    [CrossRef]
  3. A. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).
  4. B. Javidi, C. Kuo, “Joint transform image correlation using a binary spatial light modulator at the Fourier plane,” Appl. Opt. 27, 663–665 (1988).
    [CrossRef] [PubMed]
  5. F. T. S. Yu, F. Cheng, T. Nagate, D. A. Gregory, “Effect of fringe binarization of multiobject joint transform correlation,” Appl. Opt. 28, 2988–2990 (1989).
    [CrossRef] [PubMed]
  6. M. S. Alam, M. A. Karim, “Improved correlation discrimination in a multi-object bipolar joint transform correlator,” Opt. Laser Technol. 24, 45–50 (1992).
    [CrossRef]
  7. M. S. Alam, M. A. Karim, “Joint-transform correlation under varying illumination,” Appl. Opt. 32, 4351–4356 (1993).
    [CrossRef] [PubMed]
  8. M. S. Alam, O. Perez, M. A. Karim, “Preprocessed multiobject joint transform correlator,” Appl. Opt. 32, 3102–3107 (1993).
    [CrossRef] [PubMed]
  9. M. S. Alam, M. A. Karim, “Fringe-adjusted joint transform correlation,” Appl. Opt. 32, 4344–4350 (1993).
    [CrossRef] [PubMed]
  10. R. K. Wang, L. Shang, C. R. Chatwin, “Modified fringe-adjusted joint-transform correlation to accommodate noise in the input scene,” Appl. Opt. 35, 286–296 (1996).
    [CrossRef] [PubMed]
  11. M. S. Alam, “Fractional power fringe-adjusted joint transform correlation,” Opt. Eng. 34, 3208–3215 (1995).
    [CrossRef]
  12. G. Lu, Z. Zhang, S. Wu, F. T. S. Yu, “Implementation of a non-zero-order joint-transform correlator by use of phase-shifting techniques,” Appl. Opt. 36, 470–483 (1997).
    [CrossRef] [PubMed]
  13. H. J. Su, M. A. Karim, “Performance improvement of a phase-shifting joint transform correlator by use of phase-iterative techniques,” Appl. Opt. 37, 3639–3642 (1998).
    [CrossRef]
  14. H. Inbar, D. Mendlovic, E. Marom, “Error-diffusion binarization for joint transform correlators,” Appl. Opt. 32, 707–714 (1993).
    [CrossRef] [PubMed]

1998 (1)

1997 (1)

1996 (1)

1995 (1)

M. S. Alam, “Fractional power fringe-adjusted joint transform correlation,” Opt. Eng. 34, 3208–3215 (1995).
[CrossRef]

1993 (4)

1992 (1)

M. S. Alam, M. A. Karim, “Improved correlation discrimination in a multi-object bipolar joint transform correlator,” Opt. Laser Technol. 24, 45–50 (1992).
[CrossRef]

1989 (1)

1988 (1)

1984 (1)

F. T. S. Yu, X. J. Lu, “A real-time programmable joint transform correlator,” Opt. Commun. 52, 10–16 (1984).
[CrossRef]

1966 (1)

1964 (1)

A. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).

Alam, M. S.

Chatwin, C. R.

Cheng, F.

Goodman, J. W.

Gregory, D. A.

Inbar, H.

Javidi, B.

Karim, M. A.

Kuo, C.

Lu, G.

Lu, X. J.

F. T. S. Yu, X. J. Lu, “A real-time programmable joint transform correlator,” Opt. Commun. 52, 10–16 (1984).
[CrossRef]

Marom, E.

Mendlovic, D.

Nagate, T.

Perez, O.

Shang, L.

Su, H. J.

VanderLugt, A.

A. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).

Wang, R. K.

Weaver, C. S.

Wu, S.

Yu, F. T. S.

Zhang, Z.

Appl. Opt. (10)

H. Inbar, D. Mendlovic, E. Marom, “Error-diffusion binarization for joint transform correlators,” Appl. Opt. 32, 707–714 (1993).
[CrossRef] [PubMed]

M. S. Alam, O. Perez, M. A. Karim, “Preprocessed multiobject joint transform correlator,” Appl. Opt. 32, 3102–3107 (1993).
[CrossRef] [PubMed]

M. S. Alam, M. A. Karim, “Fringe-adjusted joint transform correlation,” Appl. Opt. 32, 4344–4350 (1993).
[CrossRef] [PubMed]

M. S. Alam, M. A. Karim, “Joint-transform correlation under varying illumination,” Appl. Opt. 32, 4351–4356 (1993).
[CrossRef] [PubMed]

G. Lu, Z. Zhang, S. Wu, F. T. S. Yu, “Implementation of a non-zero-order joint-transform correlator by use of phase-shifting techniques,” Appl. Opt. 36, 470–483 (1997).
[CrossRef] [PubMed]

H. J. Su, M. A. Karim, “Performance improvement of a phase-shifting joint transform correlator by use of phase-iterative techniques,” Appl. Opt. 37, 3639–3642 (1998).
[CrossRef]

R. K. Wang, L. Shang, C. R. Chatwin, “Modified fringe-adjusted joint-transform correlation to accommodate noise in the input scene,” Appl. Opt. 35, 286–296 (1996).
[CrossRef] [PubMed]

B. Javidi, C. Kuo, “Joint transform image correlation using a binary spatial light modulator at the Fourier plane,” Appl. Opt. 27, 663–665 (1988).
[CrossRef] [PubMed]

F. T. S. Yu, F. Cheng, T. Nagate, D. A. Gregory, “Effect of fringe binarization of multiobject joint transform correlation,” Appl. Opt. 28, 2988–2990 (1989).
[CrossRef] [PubMed]

C. S. Weaver, J. W. Goodman, “Technique for optically convolving two functions,” Appl. Opt. 5, 1248–1249 (1966).
[CrossRef] [PubMed]

IEEE Trans. Inf. Theory (1)

A. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).

Opt. Commun. (1)

F. T. S. Yu, X. J. Lu, “A real-time programmable joint transform correlator,” Opt. Commun. 52, 10–16 (1984).
[CrossRef]

Opt. Eng. (1)

M. S. Alam, “Fractional power fringe-adjusted joint transform correlation,” Opt. Eng. 34, 3208–3215 (1995).
[CrossRef]

Opt. Laser Technol. (1)

M. S. Alam, M. A. Karim, “Improved correlation discrimination in a multi-object bipolar joint transform correlator,” Opt. Laser Technol. 24, 45–50 (1992).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Input scene and reference for purpose of simulation.

Fig. 2
Fig. 2

Reconstructed sinusoidal fringe when R = 0.001: (a) with the initial phase calculated by phase-shift algorithm and (b) with the iterated phase.

Fig. 3
Fig. 3

Peak value of correlation versus R. Dashed curve, PSJTC method; solid curve, proposed method.

Fig. 4
Fig. 4

Improvement efficiency parameter Δ versus R.

Equations (6)

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Jnu, v=|Fu, v|2+|Ru, v|2+2|Fu, vRu, v|×cos2bu+ϕFu, v-ϕRu, v+δn,
ϕJTPS=ϕFu, v-ϕRu, v=tan-131/2J2-J1/2J0-J1-J2-2bu.
PJ=expjϕJTPS=exptan-131/2J2-J1/2J0-J1-J2-2bu
Iu, v=1+cosϕJTPS+2π/Ni,
Jsnu, v=1,Jnu, v>RJnu, v/R,otherwise,
Δ=P2-P2/P1,

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